Question

The interference pattern is obtained with two coherent light sources of intensity ratio $4: 1$. And the ratio $\frac{I_{\max }+I_{\min }}{I_{\max }-I_{\min }}$ is $\frac{5}{x}$. Then, the value of $x$ will be equal to :

• A. 3
• B. 4
• C. 2
• D. 1

Answer 1

Answer: (B)

$\frac{ I _{1}}{ I _{2}}=4$
$\frac{ I _{\max }}{ I _{\min }}=\left[\frac{\sqrt{ I _{1}}+\sqrt{ I _{2}}}{\sqrt{ I _{1}}-\sqrt{ I _{2}}}\right]^{2}$
$\frac{ I _{\max }}{ I _{\min }}=\left[\frac{2 \sqrt{ I _{2}}+\sqrt{ I _{2}}}{2 \sqrt{ I _{2}}-\sqrt{ I _{2}}}\right]^{2}$
$\frac{ I _{\max }}{ I _{\min }}=9$
$\frac{ I _{\max }}{ I _{\max }- I _{\min }}=\frac{10}{8}$
$\frac{5}{ x }=\frac{10}{8}$
$x =4$